[Banach] Abstract of a paper by Boris Rubin

[Dale Alspach]

This is an announcement for the paper "Intersection bodies and
generalized cosine transforms" by Boris Rubin.


Abstract: Intersection bodies represent a remarkable class of
geometric objects associated with sections of star bodies and
invoking Radon transforms, generalized cosine transforms, and the
relevant Fourier analysis. We review some known facts and give them
new proofs. The main focus is interrelation between generalized
cosine transforms of different kinds and their application to
investigation of certain family of intersection bodies, which we
call lambda-intersection bodies. The latter include k-intersection
bodies (in the sense of A. Koldobsky) and unit balls of finite-dimensional
subspaces of $L_p$-spaces. In particular, we show that restriction
of the spherical Radon transforms and the generalized cosine
transforms onto lower dimensional subspaces preserves their
integral-geometric structure.  We apply this result to the study
of sections of lambda-intersection bodies. A number of new
characterizations of this class of bodies and examples are given.

Archive classification:

Mathematics Subject Classification: 44A12; 52A38

Remarks: 36 pages

The source file(s), , is(are) stored in gzipped form as 0704.0061.gz
with size 31kb. The corresponding postcript file has gzipped size
195kb.

Submitted from: borisr at math.lsu.edu

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